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A General Iterative Method Based on the Hybrid Steepest Descent Scheme for Nonexpansive Mappings in Hilbert Spaces

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1 Author(s)
Ming Tian ; Coll. of Sci., Civil Aviation Univ. of China, Tianjin, China

Let H be a real Hilbert space.Suppose that T is a nonexpansive mapping on H with a fixed point, G is a L-Lipschitzian mapping on H with coefficient L > 0, and F : H → H is a k- Lipschitzian and η-strongly monotone operator with k > 0, η > O. Let 0 <; μ <; 2η/k2, 0 <; γ <; μ(η - μk2/2)/L = τ/L. We pointed out the relationship between Yamada's method and viscosity iteration and proved that the sequence {xη} generated by the iterative method xη+1 = αnγG(xn) + (I - μαnF)Txn converges strongly to a fixed point x̃ ∈ Fix(T), which solves the variational inequality ((γG - μF)x̃, x-x̃) ≤ 0, for x ∈ Fix(T).

Published in:

Computational Intelligence and Software Engineering (CiSE), 2010 International Conference on

Date of Conference:

10-12 Dec. 2010